Symmetries in Particle and String Theories

We study the space-time invariances of the bosonic relativistic particle and bosonic relativistic string using general formulations obtained by incorporating the Hamiltonian constraints into the formalism. We point out that massless particles and tensionless strings have a larger set of space-time invariances than their massive and tensionful partners, respectively. We also show that it is possible to use the reparametrization invariance of the string formulation we present to reach the classical conformal equations of motion without the use of two-dimensional Weyl scalings of the string world sheet. Finally, we show that it is possible to fix a gauge with an enlarged number of space-time invariances in which every point of the free tensionless string moves as if it were an almost-free massless particle. The existence of such a string motion agrees with what is expected from gauge theory-string duality